Question

if sin
${?}^{2}$

Answer 1

$a {sin}^{2} \alpha + b {cos}^{2} \alpha = c \\ a(1 - {cos}^{2} \alpha ) + b {cos}^{2} \alpha = c \\ {cos}^{2} \alpha (b - a) = c - a \\ cos {}^{2} \alpha = \frac{(c - a)}{(b - a)} ...(1) \\ sin {}^{2} \alpha = 1 - ({ \frac{(c - a)}{(b - a)} })^{2} ....(2)$
divide 2 @1 ..u will get it

Answer 2

$a ({ \sin( \alpha ) })^{2} + b( { \cos( \alpha ) )}^{2} = c \\ a(1 - {( \cos( \alpha )) }^{2} ) + b {( \cos( \alpha ) })^{2} = c \\ a - ({ \cos( \alpha ) )}^{2} (b - a) = c \\ { \cos( \alpha ) }^{2} = \frac{a - c}{b - a} \\ { \sec( \alpha ) }^{2} = \frac{b - a}{a - c} \\ 1 + { \tan( \alpha ) }^{2} = \frac{b - a}{a - c} \\ { \tan( \alpha ) }^{2} = \frac{b - a}{a - c} - 1 = \frac{b - a - a + c}{a - c} = \frac{b + c - 2a}{a - c}$